Journal ArticleDOI
On the Complexity of Finite Sequences
A. Lempel,Jacob Ziv +1 more
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TLDR
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented, related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated.Abstract:
A new approach to the problem of evaluating the complexity ("randomness") of finite sequences is presented. The proposed complexity measure is related to the number of steps in a self-delimiting production process by which a given sequence is presumed to be generated. It is further related to the number of distinct substrings and the rate of their occurrence along the sequence. The derived properties of the proposed measure are discussed and motivated in conjunction with other well-established complexity criteria.read more
Citations
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Journal ArticleDOI
String matching in Lempel-Ziv compressed strings
Martin Farach,Mikkel Thorup +1 more
TL;DR: This paper gives the first nontrivial compressed matching algorithm for the classic adaptive compression scheme, the LZ77 algorithm, which is known to compress more than other dictionary compression schemes, such as LZ78 and LZW, though for strings with constant per bit entropy, all these schemes compress optimally in the limit.
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Abnormal EEG complexity in patients with schizophrenia and depression
TL;DR: Compared with conventional spectral analysis, LZC was more sensitive to both the power spectrum and the temporal amplitude distribution and was associated with the ability to attend to the task and adapt the information processing system to the cognitive challenge.
Journal ArticleDOI
On compressing and indexing repetitive sequences
Sebastian Kreft,Gonzalo Navarro +1 more
TL;DR: The first self-index based on LZ77 (or LZ-End) compression is built, which in addition to text extraction offers fast indexed searches on the compressed text.
Journal ArticleDOI
Reliability of quantitative EEG features.
Steinn Gudmundsson,Thomas Philip Runarsson,Sven Sigurdsson,Gudrun Eiriksdottir,Kristinn Johnsen +4 more
TL;DR: The reliability of the qEEG features was highest for power spectral parameters, followed by regularity measures based on entropy and complexity, coherence being least reliable, which may limit their usefulness in the clinical setting.
Journal ArticleDOI
Linear time algorithms for finding and representing all the tandem repeats in a string
Dan Gusfield,Jens Stoye +1 more
TL;DR: An O(|S|)-time algorithm that operates on the suffix tree T(S) for a string S, finding and marking the endpoint of every tandem repeat that occurs in S, improves and generalizes several prior efforts to efficiently capture large subsets of tandem repeats.
References
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Journal ArticleDOI
Three approaches to the quantitative definition of information
TL;DR: In this article, three approaches to the quantitative definition of information are presented: information-based, information-aware and information-neutral approaches to quantifying information in the context of information retrieval.
Journal ArticleDOI
The definition of random sequences
TL;DR: It is shown that the random elements as defined by Kolmogorov possess all conceivable statistical properties of randomness and can equivalently be considered as the elements which withstand a certain universal stochasticity test.
Journal ArticleDOI
Process complexity and effective random tests
TL;DR: A variant of the Kolmogorov concept of complexity which yields a common theory of finite and infinite random sequences and some concepts of effective tests which are proved to be equivalent are established.
Journal ArticleDOI
Information-Theoretic Limitations of Formal Systems
TL;DR: An attempt is made to apply information-theoretic computational complexity to meta-mathematics by measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theoremic proofs.